A graphene-based plasmonic XNOR/XOR logic gate where the add-drop-channel micro-ring resonators are used as the basic unit is designed. The transmission states of graphene-based surface plasmonics can be controlled by tuning the chemical potential of graphene, and so that the XNOR and XOR operation results can be obtained simultaneously at the two output ports of this device. The simulation results show that the opening and closing of the add-drop-channel micro-ring resonators of graphene-based plasmonic waveguide can be realized when the chemical potentials are 0.677 eV and 0.95 eV, and the working frequency is 30 THz. In addition, the minimum crosstalk of the designed XNOR/XOR logic gates is -10.60 dB when the input logic states are ‘00’, ‘01’, ‘10’ and ‘11’.